MOC
1998
13 years 10 months ago
1998
Abstract. A sweep-plane algorithm of Lawrence for convex polytope computation is adapted to generate random tuples on simple polytopes. In our method an affine hyperplane is swept ...
DCG
2002
2002
A Polytope Related to Empirical Distributions, Plane Trees, Parking Functions, and the Associahedron
13 years 10 months ago
The volume of the n-dimensional polytope nx := fy 2 Rn : yi 0 and y1 + + yi x1 + + xi for all 1 i ng for arbitrary x := x1; : : : ; xn with xi 0 for all i de nes a polyn...
DCG
2000
13 years 10 months ago
2000
We show how the flag f -vector of a polytope changes when cutting off any face, generalizing work of Lee for simple polytopes. The result is in terms of explicit linear operators o...
JCT
2007
13 years 11 months ago
2007
We show that the Ehrhart h-vector of an integer Gorenstein polytope with a unimodular triangulation satisfies McMullen’s g-theorem; in particular it is unimodal. This result gen...
SIAMSC
2008
13 years 11 months ago
2008
In this study, nonnegative matrix factorization is recast as the problem of approximating a polytope on the probability simplex by another polytope with fewer facets. Working on th...
SIAMDM
2008
13 years 11 months ago
2008
Given a graph G = (V, E) with node weights v N {0}, v V , and some number F N{0}, the convex hull of the incidence vectors of all cuts (S), S V with (S) F and (V \ S) F is ...
ORL
2008
13 years 11 months ago
2008
By analogy with the conjecture of Hirsch, we conjecture that the order of the largest total curvature of the central path associated to a polytope is the number of inequalities de...
DCG
2007
13 years 11 months ago
2007
Abstract. We describe many different realizations with integer coordinates for the associahedron (i.e. the Stasheff polytope) and for the cyclohedron (i.e. the Bott-Taubes polyto...
IPL
2008
13 years 11 months ago
2008
Let P be a convex polytope in Rd , d = 3 or 2, with n vertices. We present linear time algorithms for approximating P by simpler polytopes. For instance, one such algorithm select...
COMBINATORICA
2006
13 years 11 months ago
2006
We prove that the combinatorial diameter of the skeleton of the polytope of feasible solutions of any m